3D printed Klein bottle


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The Klein bottle is a special mathematical surface, a so-called non-orientable surface. Get a 3D-printed model of this special surface and experience its uniqueness.

The Klein bottle is named after German mathematician Felix Klein who described this surface for the first time around 1882.

3D print Klein Bottle
A 3D-printed model of the Klein bottle in blue and green, 8 cm

This 8 cm large model of the Klein bottle is as light as a straw, but robust, and shows off the exceptional features of this mathematical surface. The special lattice structure of the model allows unique insights into this remarkable surface.

Mathematics: What is “non-orientable”?

Since this surface is non-orientable there is no distinction between “outside” and “inside” points of the surface. Starting at any point on the Klein bottle you can reach every other point of this surface also the point opposite the starting point. Imagine a cube where it is not possible to start with a point inside the cube and get to any cube on the outside. The (surface of a) cube is orientable.

The particular feature leading to this property of the Klein bottle is its self-intersection. Take a look at the construction of a Klein bottle from a flat surface:

Konstruktion Kleinsche Flasche
Constructing a Klein bottle via self-intersection. Source: Book “Mathematical Picture Book”
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